论文标题
GMM方法来估计随机波动的粗糙度
A GMM approach to estimate the roughness of stochastic volatility
论文作者
论文摘要
我们开发了一种GMM方法，用于估计由由不受限制的HURST指数的分数布朗运动驱动的对数正态随机波动率模型。我们表明，基于综合方差的参数估计器是一致的，在更强的条件下，渐近地正态分布。当综合方差被用离散的高频数据计算出的嘈杂的波动率量度时，我们会检查程序的行为。实现的估计器包含采样误差，这使分形系数偏向“虚幻粗糙度”。我们构建了一种分析方法来控制测量误差的影响，而无需引入滋扰参数。在一项仿真研究中，我们证明了基于整个记忆频谱的综合和实现方差的方法令人信服的小样本特性。我们显示偏差校正会减弱参数估计中的任何系统偏差。我们的程序应用于来自众多领先权益指数的经验高频数据。通过我们强大的方法，赫斯特指数的估计约为0.05，证实了随机波动性的粗糙度。
We develop a GMM approach for estimation of log-normal stochastic volatility models driven by a fractional Brownian motion with unrestricted Hurst exponent. We show that a parameter estimator based on the integrated variance is consistent and, under stronger conditions, asymptotically normally distributed. We inspect the behavior of our procedure when integrated variance is replaced with a noisy measure of volatility calculated from discrete high-frequency data. The realized estimator contains sampling error, which skews the fractal coefficient toward "illusive roughness." We construct an analytical approach to control the impact of measurement error without introducing nuisance parameters. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show the bias correction attenuates any systematic deviance in the parameter estimates. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in stochastic volatility.
